Inheritance Math Error In The Quran

ALLEGATION NO. 1: 

According to the instruction given in the Quran 4:11, 4:12 and 4:176, the sum of the fractions of inheritance is not equal to 1. In other words, the fractions of inheritance do not add up to 1. Does the God of the Quran know simple mathematics?

Answer:

It's not the God of the Quran who does not know mathematics, instead it's the people who claim the shares of inheritance do not add up to 1 do not know simple mathematics that we teach kids in school. For example, have a look at the following simple methodical question which uses the method the Quran uses to divide the property among heirs:

$40 is divided between A, B, C, and D. A gets ½ of $40. B gets ½ of what A leaves. C gets ½ of what B leaves. D gets what C leaves. Calculate how much A, B, C, and D get.

Answer:
A gets=$40x1/2=$20.
B gets=$40-$20=$20; $20x1/2=$10.
C gets=$20-$10=$10; $10x1/2=$5
D gets=$5

Now the question is if A, B, C, and D's shares of $40 add up to 1. Let's see if they do. $20+$10+$5+$5=$40.

In the Quran,
A = Creditor(s) and heir(s) of will
B = Father, mother, husband, and wife/wives
C = Son(s), daughter(s), and People with whom the deceased made contract
D = Brother(s) and sister(s)

The list of heirs of the inheritance and their priority of rights on inheritance are mentioned in the Quran:

Group 1:
(1) Creditor(s): Creditor(s) and heir(s) of will get their share of the inheritance before everybody else. [See verse 4:11 and 4:12]
(2) Heir(s) of will: Creditor(s) and heir(s) of will get their share of the inheritance before everybody else. [See verse 4:11 and 4:12]

Group 2:
(1) Father: Father, mother, husband, and wife/wives get their share of the inheritance from what is left by creditor(s) and heir(s) of will. [See verse 4:11 and 4:12]
(2) Mother: Father, mother, husband, and wife/wives get their share of the inheritance from what is left by creditor(s) and heir(s) of will. [See verse 4:11 and 4:12]
(3) Husband: Father, mother, husband, and wife/wives get their share of the inheritance from what is left by creditor(s) and heir(s) of will. [See verse 4:11 and 4:12]
(4) Wife/Wives: Father, mother, husband, and wife/wives get their share of the inheritance from what is left by creditor(s) and heir(s) of will. [See verse 4:11 and 4:12]

Group 3:
(1) Son(s): Son(s), daughter(s), and People with whom the deceased made contract get their share of the inheritance from what is left by father, mother, husband, and wife/wives. [See verse 4:7 and 4:33]
(2) Daughter(s): Son(s), daughter(s), and People with whom the deceased made contract get their share of the inheritance from what is left by father, mother, husband, and wife/wives. [See verse 4:7 and 4:33]
(3) People with whom the deceased made contract: Son(s), daughter(s), and People with whom the deceased made contract get their share of the inheritance from what is left by father, mother, husband, and wife/wives. [See verse 4:7 and 4:33]

Note: An example of People with whom the deceased made contract is business partner(s). Note that there are two things a deceased can owe his/her business partners(s): (1) money (2) time. If the deceased owe his/her business partners money, then his/her business partners will be considered as Creditor(s) but if the deceased owe his/her business partners time, then his/her business partners will be considered as People with whom the deceased made contract. If A makes a partnership business agreement with B till 2012 but A dies in 2010, then A owes B 2 years (2012 -- 2010 = 02) of time in agreement.

Group 4:
(1) Brother(s):
• If there is no son or daughter, then brother(s) and sister(s) qualify as "Group 3" heirs and get their share of the inheritance from what is left by father, mother, husband, and wife/wives. [See verse 4:176]
• If there is no son, daughter, father, or mother, then brother(s) and sister(s) qualify as "Group 2" heirs and get their share of the inheritance from what is left by creditor(s) and heir(s) of will. [See verse 4:12]
(2) Sister(s):
• If there is no son or daughter, then brother(s) and sister(s) qualify as "Group 3" heirs and get their share of the inheritance from what is left by father, mother, husband, and wife/wives. [See verse 4:176]
• If there is no son, daughter, father, or mother, then brother(s) and sister(s) qualify as "Group 2" heirs and get their share of the inheritance from what is left by creditor(s) and heir(s) of will. [See verse 4:12]

ALLEGATION NO. 2:

The names of some of the heirs are mentioned but the quantities of their shares are not mentioned.

Answer: Again, I want to remind you that people who make these allegations do not know simple mathematics that we teach kids in school. For example -

Sample allegation no. (i): Quran says $21 is divided between A and B. It says A gets 1/3 of $21 but it does not say how much B gets. Therefore it is an error of Quran because we do not know how much B gets.

Answer to the allegation: To answer this allegation, have a look at the simple mathematical question below:
Question: $21 is divided between A and B. A gets 1/3 of $21.  How much A and B get?
Answer: A gets=$21x1/3=$7. B gets=$21-$7=$14.

Sample allegation no. (ii): Quran says $30 is divided between A, B, and C. But it does not say who gets C's share of $30 when C does not exist. Therefore, Quran is wrong.

Answer to the allegation: To answer this allegation, have a look at the simple mathematical equation below:
Heirs' right on property = A's right on property + B's right on property + C's right on property.

If heir C doesn't exist, we can say C has zero right on property. In that case -
Heirs' right on property = A's right on property + B's right on property + 0 = A's right on property + B's right on property.

Therefore, A and B will share C's share of the property if C does not exist.

Sample allegation no. (iii): When answering to the "Sample allegation no. (ii)", you said if A, B, and C are the heirs of the property and if C does not exist, then A and B will share C's share of the property. But sometimes Quran says D will share C's share of the property if C does not exist. Is not it unfair to A and B? Because you prove with mathematical equation that A and B should share C's share of the property if C does not exist.
Answer to the allegation: To answer this allegation, have a look at the simple mathematical equation below:
If E=A+B+C and C=D, then
E=A+B+D

If it says A, B, and C are the heirs of the property ($30) and ask you what to do with C's share of the property, then you let A and B share C's share of the property.

But if it says (i) A, B, and C are the heirs of the property ($30) and (ii) D substitutes C when C does not exist, then you let D have C's share of the property.

Both "letting A and B share C's share of the property" and "letting D have C's share of the property" are correct depending on the terms given on different scenarios.

REFERENCES:

"Instructs you God concerning your children - for the male like (the) portion (of) two females. But if there are (only) women more (than) two, then for them two thirds (of) what he left. And if (there) is (only) one, then for her (is) half. And for his parents, for each one of them a sixth of what (is) left, if is for him a child. But if not is for him any child  and inherit[ed] him his parents, then for his mother (is) one third. And if are for him brothers and sisters, then for his mother (is) the sixth from after any will he has made [of which] or any debt. Your parents and your children -- not you know which of them (is) nearer to you (in) benefit. An obligation from God Indeed, God is All-Knowing, All-Wise." [Quran 4:11 - word for word translation]

"And for you (is) half (of) what (is) left by your wives if not is for them a child. But if is for them a child, then for you (is) the fourth of what they left, from after any will they have made [for which] or any debt. And for them (is) the fourth of what you left, if not is for you a child. But if is for you a child, then for them (is) the eighth of what you left from after any will you have made [for which] or any debt. And if [is] a man (whose wealth) is to be inherited (has) no parent or child or a women and for him (is) a brother or a sister, then for each one of (the) two (is) the sixth. But if they are more than that, then they (are) partners in the third, from after any will was made [for which] or any debt without (being) harmful. An ordinance from God. And God (is) All-Knowing, All-Forbearing." [Quran 4:12 - word for word translation]

"They seek your ruling." Say, God gives you a ruling concerning the kalala if a man died (and) not he has a child and he has a sister, then for her (is) a half (of) what he left. And he will inherit from her if not is for her a child. But if there were two females then for them two thirds of what he left. But if they were brothers and sisters men and women, then the male will have like share (of) the two females. Makes clear God to you lest you go astray. And God of every thing (is) All-Knower." (Quran 4:176 - word for word translation)

"And all We (have) made heirs of what (is) left (by) the (their) parents and the relatives. And those whom contracted your right hands - then give them their share. Indeed, God is over everything a witness. [Quran 4:33- word for word translation]

"For the men (there is) a portion of what (is) left (by) the parents, and the near relatives and for the women a portion of what (is) left (by) parents and the near relatives of what (is) little of it or much -- a portion determinate." [Quran 4:7- word for word translation]